×

General asymptotic confidence bands based on kernel-type function estimators. (English) Zbl 1125.62314

Summary: We establish uniform and non-uniform asymptotic simultaneous confidence bands for functionals of the distribution based on kernel-type estimators, which include the Nadaraya-Watson kernel estimators of regression functions and the Akaike-Parzen-Rosenblatt kernel density estimators. Our theorems, based upon functional limit laws derived by modern empirical process theory, allow data-driven local bandwidths for these statistics.

MSC:

62G07 Density estimation
62G15 Nonparametric tolerance and confidence regions
62G08 Nonparametric regression and quantile regression
60F15 Strong limit theorems

Software:

KernSmooth
Full Text: DOI